Modeling of a Fluid with Pressure-Dependent Viscosity in Hele-Shaw Flow
We investigate the Hele-Shaw flow of fluids whose viscosity depends on pressure, i.e., piezo-viscous fluids, near the tip of a sharp edge. In particular, we consider both cases of two-dimensional symmetric and antisymmetric flows. To obtain the pressure field, we provide a procedure that is based on...
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MDPI AG
2024-10-01
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| author | Benedetta Calusi Liviu Iulian Palade |
| author_facet | Benedetta Calusi Liviu Iulian Palade |
| author_sort | Benedetta Calusi |
| collection | DOAJ |
| description | We investigate the Hele-Shaw flow of fluids whose viscosity depends on pressure, i.e., piezo-viscous fluids, near the tip of a sharp edge. In particular, we consider both cases of two-dimensional symmetric and antisymmetric flows. To obtain the pressure field, we provide a procedure that is based on the method of separation of variables and does not depend on a specific choice of the expression for the pressure-dependent viscosity. Therefore, we show the existence of a general procedure to investigate the behavior of piezo-viscous fluids in Hele-Shaw flow and its solution near a sharp corner. The results are applied to the case of an exponential dependence of viscosity on pressure as an example of exact solutions for the pressure field. |
| format | Article |
| id | doaj-art-a568065eaed24cb7b4e2ba121f5f6939 |
| institution | OA Journals |
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| language | English |
| publishDate | 2024-10-01 |
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| spelling | doaj-art-a568065eaed24cb7b4e2ba121f5f69392025-08-20T02:01:10ZengMDPI AGModelling2673-39512024-10-01541490150410.3390/modelling5040077Modeling of a Fluid with Pressure-Dependent Viscosity in Hele-Shaw FlowBenedetta Calusi0Liviu Iulian Palade1Dipartimento di Matematica e Informatica “Ulisse Dini”, Università degli Studi di Firenze, Viale Morgagni 67/a, 50134 Firenze, ItalyInstitut Camille Jordan CNRS UMR 5208, INSA-Lyon & Pôle de Mathématiques, Université de Lyon, 21 Avenue Jean Capelle, 69621 Villeurbanne Cedex, FranceWe investigate the Hele-Shaw flow of fluids whose viscosity depends on pressure, i.e., piezo-viscous fluids, near the tip of a sharp edge. In particular, we consider both cases of two-dimensional symmetric and antisymmetric flows. To obtain the pressure field, we provide a procedure that is based on the method of separation of variables and does not depend on a specific choice of the expression for the pressure-dependent viscosity. Therefore, we show the existence of a general procedure to investigate the behavior of piezo-viscous fluids in Hele-Shaw flow and its solution near a sharp corner. The results are applied to the case of an exponential dependence of viscosity on pressure as an example of exact solutions for the pressure field.https://www.mdpi.com/2673-3951/5/4/77Hele-Shaw flowsymmetrical and antisymmetrical flowslubrication approximationpressure-dependent viscositypiezo-viscous fluids |
| spellingShingle | Benedetta Calusi Liviu Iulian Palade Modeling of a Fluid with Pressure-Dependent Viscosity in Hele-Shaw Flow Modelling Hele-Shaw flow symmetrical and antisymmetrical flows lubrication approximation pressure-dependent viscosity piezo-viscous fluids |
| title | Modeling of a Fluid with Pressure-Dependent Viscosity in Hele-Shaw Flow |
| title_full | Modeling of a Fluid with Pressure-Dependent Viscosity in Hele-Shaw Flow |
| title_fullStr | Modeling of a Fluid with Pressure-Dependent Viscosity in Hele-Shaw Flow |
| title_full_unstemmed | Modeling of a Fluid with Pressure-Dependent Viscosity in Hele-Shaw Flow |
| title_short | Modeling of a Fluid with Pressure-Dependent Viscosity in Hele-Shaw Flow |
| title_sort | modeling of a fluid with pressure dependent viscosity in hele shaw flow |
| topic | Hele-Shaw flow symmetrical and antisymmetrical flows lubrication approximation pressure-dependent viscosity piezo-viscous fluids |
| url | https://www.mdpi.com/2673-3951/5/4/77 |
| work_keys_str_mv | AT benedettacalusi modelingofafluidwithpressuredependentviscosityinheleshawflow AT liviuiulianpalade modelingofafluidwithpressuredependentviscosityinheleshawflow |